Question: Solve for $x$ and $y$ using elimination. ${-5x-2y = -46}$ ${3x+2y = 34}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-2x = -12$ $\dfrac{-2x}{{-2}} = \dfrac{-12}{{-2}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-5x-2y = -46}\thinspace$ to find $y$ ${-5}{(6)}{ - 2y = -46}$ $-30-2y = -46$ $-30{+30} - 2y = -46{+30}$ $-2y = -16$ $\dfrac{-2y}{{-2}} = \dfrac{-16}{{-2}}$ ${y = 8}$ You can also plug ${x = 6}$ into $\thinspace {3x+2y = 34}\thinspace$ and get the same answer for $y$ : ${3}{(6)}{ + 2y = 34}$ ${y = 8}$